Abstract Samuel introduced the notions of fuzzy vector lattices and fuzzy points of fuzzy vector lattices. He considered unique extensions of fuzzy Daniell integrals (i.e. positive linear σ -order continuous maps) defined on sets of fuzzy points to spaces that behave like L 1 -spaces. His arguments hinge on the fact that sets of fuzzy points of a fuzzy vector lattice form vector lattices. We show, by means of a counter example, that the set of fuzzy points of a fuzzy vector lattice does not form a vector lattice. Consequently, Samuel's fuzzy Daniell integrals need not be linear.